Journal of Applied Probability

Stopping probabilities for patterns in Markov chains

Renato Jacob Gava and Danilo Salotti

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Abstract

Consider a sequence of Markov-dependent trials where each trial produces a letter of a finite alphabet. Given a collection of patterns, we look at this sequence until one of these patterns appears as a run. We show how the method of gambling teams can be employed to compute the probability that a given pattern is the first pattern to occur.

Article information

Source
J. Appl. Probab., Volume 51, Number 1 (2014), 287-292.

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771430

Digital Object Identifier
doi:10.1239/jap/1395771430

Mathematical Reviews number (MathSciNet)
MR3189458

Zentralblatt MATH identifier
1291.60147

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60G42: Martingales with discrete parameter

Keywords
Stopping time waiting time gambling team martingale Markov chain pattern stopping probability

Citation

Gava, Renato Jacob; Salotti, Danilo. Stopping probabilities for patterns in Markov chains. J. Appl. Probab. 51 (2014), no. 1, 287--292. doi:10.1239/jap/1395771430. https://projecteuclid.org/euclid.jap/1395771430


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